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of the wave properties in the surface layers. In particular, upward propagating
high-frequency ( ! > ! c) waves are re
ected and refracted at the a=csurface,
where MHD mode conversion occurs. Finsterle et al. (2004b) used multi-height
observations of solar oscillations to map the a=csurface in active regions,
called the `magnetic canopy'. The travel time measured between two observation
heights in the solar atmospheres was used to derive the propagation properties of
the waves between these two layers. When both heights are above the a=clayer,
waves are evanescent and the travel time vanishes. Using combinations of three
heights, they nd that in sunspots and active regions the canopy deeps below the
base of the photosphere by several hundred km, while it is above 1000 km in the
quiet Sun.
7 EXTENDED FLOWS AROUND ACTIVE REGIONS
In this section, we describe
ows around large complexes of magnetic activity.
These
ows should not be confused with the (smaller scale) moat
ow around
individual sunspots, which was discussed in Section 6.30 Gizon, Birch & Spruit
7.1 Surface In
ows, Deeper Out
ows
Using f-mode time-distance helioseismology, Gizon, Duvall & Larsen (2001) de-
tected weak50 m s1surface
ows that converge toward active regions ( Fig-
ure 18 ). These in
ows, which exist as far as 30from the centers of active
regions, are also seen in ring diagram analyses (e.g. Haber et al. 2001, 2004,
Komm et al. 2007). In fact, Hindman et al. (2004) showed that the time-distance
and ring-diagram methods give nearly identical results near the surface. These
near-surface
ows also agree reasonably well with the motion of supergranules
(Svanda, Zhao & Kosovichev 2007). The converging
ows near the surface are
accompanied by cyclonic
ows with vorticity of order 107s1(Komm et al.
2007).
At depths in the range of about 10 Mm to 15 Mm, diverging
ows from active
regions have been inferred using the time-distance (Zhao & Kosovichev 2004) and
ring-diagram (Haber et al. 2004) methods. These diverging
ows typically have
amplitudes of order 50 m s1. Komm et al. (2004) used ring-diagram measure-
ments together with the constraint of mass conservation to infer downward
ows
of order 1 m s1, at depths less than about 10 Mm, in and around active regions.
Below this depth, the active regions tend to show up
ows.
The observations are summarized in Figure 19 , which shows the organization
of horizontal
ows around a particular complex of magnetic activity at three
dierent depths. The
ow patterns are consistent from day to day, despite the
presence of supergranulation noise.
7.2 Flows due to Thermal Eects of Magnetic Fields
A diagnostically important class of
ows are those associated with thermal eects
due to magnetic elds, such as heating by dissipation of magnetic energy or the
enhanced radiative loss of small scale magnetic elds at the surface. On interme-
diate to large scales and time scales exceeding the rotation period approximate
geostrophic balance holds in the convection zone. Hence
ows of the thermal
wind type must accompany thermal disturbances on those scales. For example,
the enhanced radiative loss from the small scale magnetic eld in active regions
has a cooling eect that should drive an in
ow at the surface and a circulation
in the cyclonic sense around the active region (Spruit 2003), as in low pressure
systems in the Earth's atmosphere. This may be an explanation for the
ows
described in the previous section.
8 GLOBAL SCALES
The dominant global-scale
ows in the Sun are the dierential rotation and the
meridional
ow. Helioseismic measurements made over long time scales (a few so-
lar rotation periods) eectively remove the contribution of small-scale convectiveLocal Helioseismology 31

ows and active region
ows and allow high precision studies of these global-scale

ows. Both rotation and the meridional
ow show small variations with the solar
cycle.
8.1 Dierential Rotation
The North-South symmetric component of internal dierential rotation has been
measured using global helioseismology (cf. review by Thompson et al. 2003).
The solar rotation rate depends strongly on latitude in the convection zone, with
the equator rotating more quickly than the poles. The rotation rate shows only
a weak radial shear in the bulk of the convection zone. There is strong radial
shear in the very near surface layers (top 35 Mm, Schou et al. 1998), and in the
tachocline where the dierentially rotating convection zone meets the uniformly
rotating radiative zone. The tachocline plays an important role in most dynamo
theories of the solar cycle.
As the dierential rotation is well known, it provides an important test of local
helioseismic methods. Giles, Duvall & Scherrer (1998) measured rotation with
time-distance helioseismology applied to MDI data and found good qualitative
agreement with the results of global helioseismology. Basu, Antia & Tripathy
(1999) and Gonz alez Hern andez et al. (2006) both used ring-diagram analysis
to study the dierential rotation in the near-surface shear layer. These studies
found rotation rates that essentially agreed with those inferred from global he-

of the wave properties in the surface layers. In particular, upward propagating

high-frequency ( ! > ! c) waves are re

ected and refracted at the a=csurface,

where MHD mode conversion occurs. Finsterle et al. (2004b) used multi-height

observations of solar oscillations to map the a=csurface in active regions,

called the `magnetic canopy'. The travel time measured between two observation

heights in the solar atmospheres was used to derive the propagation properties of

the waves between these two layers. When both heights are above the a=clayer,

waves are evanescent and the travel time vanishes. Using combinations of three

heights, they nd that in sunspots and active regions the canopy deeps below the

base of the photosphere by several hundred km, while it is above 1000 km in the

quiet Sun.

7 EXTENDED FLOWS AROUND ACTIVE REGIONS

In this section, we describe

ows around large complexes of magnetic activity.

These

ows should not be confused with the (smaller scale) moat

ow around

individual sunspots, which was discussed in Section 6.30 Gizon, Birch & Spruit

7.1 Surface In

ows, Deeper Out

ows

Using f-mode time-distance helioseismology, Gizon, Duvall & Larsen (2001) de-

tected weak50 m s1surface

ows that converge toward active regions ( Fig-

ure 18 ). These in

ows, which exist as far as 30from the centers of active

regions, are also seen in ring diagram analyses (e.g. Haber et al. 2001, 2004,

Komm et al. 2007). In fact, Hindman et al. (2004) showed that the time-distance

and ring-diagram methods give nearly identical results near the surface. These

near-surface

ows also agree reasonably well with the motion of supergranules

(Svanda, Zhao & Kosovichev 2007). The converging

ows near the surface are

accompanied by cyclonic

ows with vorticity of order 107s1(Komm et al.

2007).

At depths in the range of about 10 Mm to 15 Mm, diverging

ows from active

regions have been inferred using the time-distance (Zhao & Kosovichev 2004) and

ring-diagram (Haber et al. 2004) methods. These diverging

ows typically have

amplitudes of order 50 m s1. Komm et al. (2004) used ring-diagram measure-

ments together with the constraint of mass conservation to infer downward

ows

of order 1 m s1, at depths less than about 10 Mm, in and around active regions.

Below this depth, the active regions tend to show up

ows.

The observations are summarized in Figure 19 , which shows the organization

of horizontal

ows around a particular complex of magnetic activity at three

dierent depths. The

ow patterns are consistent from day to day, despite the

presence of supergranulation noise.

7.2 Flows due to Thermal Eects of Magnetic Fields

A diagnostically important class of

ows are those associated with thermal eects

due to magnetic elds, such as heating by dissipation of magnetic energy or the

enhanced radiative loss of small scale magnetic elds at the surface. On interme-

diate to large scales and time scales exceeding the rotation period approximate

geostrophic balance holds in the convection zone. Hence

ows of the thermal

wind type must accompany thermal disturbances on those scales. For example,

the enhanced radiative loss from the small scale magnetic eld in active regions

has a cooling eect that should drive an in

ow at the surface and a circulation

in the cyclonic sense around the active region (Spruit 2003), as in low pressure

systems in the Earth's atmosphere. This may be an explanation for the

ows

described in the previous section.

8 GLOBAL SCALES

The dominant global-scale

ows in the Sun are the dierential rotation and the

meridional

ow. Helioseismic measurements made over long time scales (a few so-

lar rotation periods) eectively remove the contribution of small-scale convectiveLocal Helioseismology 31

ows and active region

ows and allow high precision studies of these global-scale

ows. Both rotation and the meridional

ow show small variations with the solar

cycle.

8.1 Dierential Rotation

The North-South symmetric component of internal dierential rotation has been

measured using global helioseismology (cf. review by Thompson et al. 2003).

The solar rotation rate depends strongly on latitude in the convection zone, with

the equator rotating more quickly than the poles. The rotation rate shows only

a weak radial shear in the bulk of the convection zone. There is strong radial

shear in the very near surface layers (top 35 Mm, Schou et al. 1998), and in the

tachocline where the dierentially rotating convection zone meets the uniformly

rotating radiative zone. The tachocline plays an important role in most dynamo

theories of the solar cycle.

As the dierential rotation is well known, it provides an important test of local

helioseismic methods. Giles, Duvall & Scherrer (1998) measured rotation with

time-distance helioseismology applied to MDI data and found good qualitative

agreement with the results of global helioseismology. Basu, Antia & Tripathy

(1999) and Gonz alez Hern andez et al. (2006) both used ring-diagram analysis

to study the dierential rotation in the near-surface shear layer. These studies

found rotation rates that essentially agreed with those inferred from global he-